Quantum bridges in phase space: interference and nonclassicality in strong-field enhanced ionisation

Abstract

We perform a phase-space analysis of strong-field enhanced ionisation in molecules, with emphasis on quantum-interference effects. Using Wigner quasi-probability distributions and the quantum Liouville equation, we show that the momentum gates reported in a previous publication (Takemoto and Becker 2011 Phys. Rev. A 84 023401) may occur for static driving fields, and even for no external field at all. Their primary cause is an interference-induced bridging mechanism that occurs if both wells in the molecule are populated. In the phase-space regions for which quantum bridges occur, the Wigner functions perform a clockwise rotation whose period is intrinsic to the molecule. This evolution is essentially non-classical and non-adiabatic, as it does not follow equienergy curves or field gradients. Quasi-probability transfer via quantum bridges is favoured if the electron's initial state is either spatially delocalised, or situated at the upfield molecular well. Enhanced ionisation results from the interplay of this cyclic motion, adiabatic tunnel ionisation and population trapping. Optimal conditions require minimising population trapping and using the bridging mechanism to feed into ionisation pathways along the field gradient.

Attoscience in phase space

“…For systems with more than one centre, such as in diatomic molecules, Wigner quasiprobability distributions have been employed in the context of enhanced ionisation [74,75,78]. Roughly speaking, enhanced ionisation means that, for specific internuclear separations, ionisation rates in a stretched molecule are considerably higher than those in an atom with a similar ionisation potential [138].…”

“…Further work, however, showed that the momentum gates are intrinsic to the molecular sys-tem and exist even for static fields, or no fields at all. Thereby, quantum interference plays an important role by providing a bridge for quasiprobability to flow from one molecular well to the other [78], and the frequencies can be estimated for double-well potential models [139]. Further studies of nonadiabatic effects and bifurcation in strong-field ionisation were conducted in [77].…”

“…These are used to classify regions with qualitatively different behaviours and understand how processes such tunnelling and rescattering unfold. For details, we refer to the original publications [76,78,82,139]. We also intend to go beyond these articles, by bringing together aspects that have not been emphasised so far.…”

“…This definition of ionisation rate was used in the seminal paper [138] in the context of enhanced ionisation of molecules, and in our previous publications [78,139].…”

“…Still, some groups have explored phase space dynamics in a strong-field context. This includes stabilisation [69][70][71][72], strong-field ionisation [73][74][75][76][77][78], high-order harmonic generation [79][80][81][82][83], laser-induced core dynamics [84,85], rescattering [79,80,[86][87][88][89], nonsequential double ionisation [90][91][92][93][94][95][96][97][98][99][100][101][102][103][104][105][106], or in connection with initial-value representations in strong fields [76,[107][108][109][110]. Furthermore, the growing interest in free-electron lasers (FELs) means that the tools employed in quantum optics are being explored in the X-ray and extreme ultraviolet (XUV) regime [111,112].…”